We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) method based on conditional quantile regression. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension, conditioned on the data and previous posterior dimensions. Posterior samples are obtained by interpolating the predicted quantiles using monotonic cubic Hermite spline, with specific treatment for the tail behavior and multi-modal distributions. We introduce an alternative definition for the Bayesian credible region using the local Cumulative Density Function (CDF), offering substantially faster evaluation than the traditional Highest Posterior Density Region (HPDR). In case of limited simulation budget and/or known model misspecification, a post-processing calibration step can be integrated into NQE to ensure the unbiasedness of the posterior estimation with negligible additional computational cost. We demonstrate that NQE achieves state-of-the-art performance on a variety of benchmark problems.

翻译：本文提出神经分位数估计（Neural Quantile Estimation, NQE），一种基于条件分位数回归的新型仿真推断方法。NQE以自回归方式学习后验分布各维度的一维分位数，其条件为观测数据及已处理的后验维度。后验样本通过使用单调三次Hermite样条插值预测的分位数获得，并对尾部行为与多峰分布进行了特殊处理。我们利用局部累积分布函数提出了一种贝叶斯可信区域的替代定义，其计算速度显著快于传统的最高后验密度区域。在仿真预算有限和/或已知模型设定存在偏误的情况下，可将后处理校准步骤整合至NQE中，以可忽略的额外计算成本确保后验估计的无偏性。实验表明，NQE在多种基准问题上均达到了最先进的性能水平。